What does Professor Henry Jones Sr mean of "illumination"?

It doesn't mean anything. Tobasco below probably is correct with the response of "enlightenment". I love the Indiana Jones movies, but these movies try to tie in to western beliefs without actually getting into them.

Maybe the enlightenment is in the finding of great historical artifact, but as you can see by the fates of the those involved in that last scene - it's honest appraisal, not the search for gold - that is the most important thing.

The thing about the Holy Grail is, that it's irrelevant. Finding it would be an interesting historical and archeological find, but there's no spiritual power in the cup that Jesus used for the first Communion. The power of salvation is through faith in him - the relics are just relics. Interesting, worth the effort, but only so.

I think this is supposed to be one of the "multiple viewings" easter eggs.
On the first pass you're supposed to get the impression that "he who illuminated this" is god and you want enlightened from God as well.
Subsequent passes (I think} are supposed to yield that illuminated in the first sense is the person who wrote the text and provided flourishes in the right places.. and was the knight that Jones met. Who made him realize the limit to/burden of maintaining or keeping the grail and how that would impact his relationships with people, who he cared about et al.

So once he gets through all that and can let go of the grail to return to stable ground with his dad, he's now wiser and has been illuminated.

I think he means he found clarity in his life. But I think his illumination also refers to his understanding and discovery of the Grail and its location. That diary might as well have been the Grail, with how important it was.

A play on words, possibly. Illumination can mean both illustrating a manuscript and enlightebment. But i don;t remember the scene, so I'm not sure. :(

Illumination possibly refers to ‘let there be light’ in other words coming closer to God, an being illuminated as a result.

It was probably an illuminated manuscript, common in the Catholic church before the 13th century.

https://en.wikipedia.org/wiki/Illuminated_manuscript

Better ask yourself, why your own question! For you are saying the same thing, just in different words.

Enlightenment?